so technically unless you skill Tidebringer and have it on CD you won't gain the +dmg or +% of QB,IT or BF.

It seems that the problem is connected to the fact that the Quell passive is supposed to not stack with the Tidebringer effect itself on the procc/cast on purpose. (which is actually quite absurd when you consider that Quell passives from multiple sources i.e QB and IT are stackable.)
A similar case for a "special" autocast would be Jakiro (CD-based autocast combined with a visually seen buff when ready) where the Quell passive works as intended on normal autohits.
So i believe it is just a minor error that comes from the problem that the Tidebringer effect itself is puposely not stackable with the Quell passive to avoid the abuse of such use for the "cleave" on hero-targets (using Tidebringer purposely on non-hero units to increase the damage for hero units in the Tidebringer rather than the fact that Tidebringer is actually considered a cleave because the Quell passive is working intended with those (Battlefury, Sven, Magnus etc.)